Problem: $f(x) = 3x^2+12x+5 $ What is the value of the discriminant of $f$ ?
The ${\text{discriminant}}$ is a part of the quadratic formula. The sign of the discriminant tells us whether there are two roots, one root, or no roots. $\dfrac{-b\pm{\sqrt{\overbrace{{b^2-4ac}}^{\text{discriminant}}}}}{2a}$ Discriminant Roots Positive Two real roots Zero One repeated real root Negative No real root Let's find the discriminant of $f$ : $\begin{aligned} {b^2-4ac}&=12^2-4\cdot3\cdot5 \\\\ &=144-60 \\\\ &={84} \end{aligned}$ So how many real number zeros does $f$ have? Since the discriminant is positive, $f$ has $2$ distinct real number zeros. In conclusion: The discriminant of $f$ is ${84}$. $f$ has $2$ distinct real number zeros.